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<p>A critical challenge in mineral processing is the accurate estimation of fundamental sampling error (FSE). Currently this challenge is addressed by two dominant yet disconnected paradigms: Gy’s liberation-based theory and empirical nugget effect analysis. The liberation-corrected model reveals an ore’s intrinsic homogeneity but cannot predict sampling error for intermediate crush sizes. Conversely, the nominal nugget model measures observed heterogeneity but fails to distinguish between intrinsic clustering and liberation state. This paper introduces a novel integrated framework that synergizes these approaches to resolve this disconnect. We re-analyse a comprehensive gold ore dataset (448 samples across 14 size fractions) using both the liberation-corrected FSE model and the Poisson-based nominal nugget model. Our analysis demonstrates that the ore is intrinsically homogeneous (intrinsic homogeneity index = 0.68%) yet exhibits a strong, liberation-dependent empirical nugget effect, where the nominal nugget size decreases predictably with fragment size, diagnosing a liberation-limited system. A global sensitivity analysis confirms that fragment size is the dominant controllable parameter for sampling variance, accounting for 68–88% of output variance across comminution stages. The integrated framework provides a diagnostic tool to unequivocally distinguish between fundamentally heterogeneous and liberation-limited ores. This enables a more rational, data-driven, and cost-effective optimization of comminution and sampling protocols, with estimated annual savings exceeding US$120,000 for mid-sized operations, moving beyond the limitations of single-model approaches to achieve new levels of precision and efficiency in resource evaluation.</p>

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The Hidden Variable in Sampling Protocols: A Review of Liberation Evolution through Subsampling and Comminution

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月28日

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  • Richard Minnitt,
  • Pentti Minkkinen

摘要

A critical challenge in mineral processing is the accurate estimation of fundamental sampling error (FSE). Currently this challenge is addressed by two dominant yet disconnected paradigms: Gy’s liberation-based theory and empirical nugget effect analysis. The liberation-corrected model reveals an ore’s intrinsic homogeneity but cannot predict sampling error for intermediate crush sizes. Conversely, the nominal nugget model measures observed heterogeneity but fails to distinguish between intrinsic clustering and liberation state. This paper introduces a novel integrated framework that synergizes these approaches to resolve this disconnect. We re-analyse a comprehensive gold ore dataset (448 samples across 14 size fractions) using both the liberation-corrected FSE model and the Poisson-based nominal nugget model. Our analysis demonstrates that the ore is intrinsically homogeneous (intrinsic homogeneity index = 0.68%) yet exhibits a strong, liberation-dependent empirical nugget effect, where the nominal nugget size decreases predictably with fragment size, diagnosing a liberation-limited system. A global sensitivity analysis confirms that fragment size is the dominant controllable parameter for sampling variance, accounting for 68–88% of output variance across comminution stages. The integrated framework provides a diagnostic tool to unequivocally distinguish between fundamentally heterogeneous and liberation-limited ores. This enables a more rational, data-driven, and cost-effective optimization of comminution and sampling protocols, with estimated annual savings exceeding US$120,000 for mid-sized operations, moving beyond the limitations of single-model approaches to achieve new levels of precision and efficiency in resource evaluation.